Numbers in Indian & International Systems

Write the following numerals using the Indian System or International system (as required) in words:

(i) 4,35,342

(ii) 36,71,430

(iii) 4,28,30,004

(iv) 75,132,684

(v) 815,906

(vi) 5,420,700

Answer

The position of the commas tells us which system to use — Indian commas (grouped as 3, 2, 2, .. from the right) for parts (i) to (iii) and International commas (grouped as 3, 3, 3, .. from the right) for parts (iv) to (vi).

(i) In the Indian system, 4,35,342 is grouped as:

∴ 4,35,342 = Four lakh thirty five thousand three hundred forty two.

(ii) In the Indian system, 36,71,430 is grouped as:

∴ 36,71,430 = Thirty six lakh seventy one thousand four hundred thirty.

(iii) In the Indian system, 4,28,30,004 is grouped as:

∴ 4,28,30,004 = Four crore twenty eight lakh thirty thousand four.

(iv) In the International system, 75,132,684 is grouped as:

∴ 75,132,684 = Seventy five million one hundred thirty two thousand six hundred eighty four.

(v) In the International system, 815,906 is grouped as:

∴ 815,906 = Eight hundred fifteen thousand nine hundred six.

(vi) In the International system, 5,420,700 is grouped as:

∴ 5,420,700 = Five million four hundred twenty thousand seven hundred.

Write the following numbers, placing the commas, according to the Indian system:

(i) 835629

(ii) 35640254

(iii) 2826040

Answer

In the Indian system, starting from the right, the first comma is placed after 3 digits and then after every 2 digits.

(i) 835629 → mark off 629, then 35, then 8.

∴ 835629 = 8,35,629.

(ii) 35640254 → mark off 254, then 40, then 56, then 3.

∴ 35640254 = 3,56,40,254.

(iii) 2826040 → mark off 040, then 26, then 28.

∴ 2826040 = 28,26,040.

Write the following numbers, by placing the commas, according to the International system:

(i) 6509820

(ii) 428140584

(iii) 63560981

Answer

In the International system, starting from the right, a comma is placed after every 3 digits.

(i) 6509820 → mark off 820, then 509, then 6.

∴ 6509820 = 6,509,820.

(ii) 428140584 → mark off 584, then 140, then 428.

∴ 428140584 = 428,140,584.

(iii) 63560981 → mark off 981, then 560, then 63.

∴ 63560981 = 63,560,981.

Fill in the blanks as indicated:

(i) Four lakh sixty seven thousand three hundred six.

= ............ (In Indian numeral form)

= ............ (In International numeral form)

= ............ (In International numeration)

(ii) Thirteen lakh forty five.

= ............ (In Indian numeral form)

= ............ (In International numeral form)

= ............ (In International numeration)

Answer

(i) Four lakh sixty seven thousand three hundred six.

Writing the digits in the place value chart of the Indian system :

So, the number in Indian numeral form = 4,67,306.

Placing the commas according to the International system (after every 3 digits from the right) = 467,306.

In International numeration, 467,306 = Four hundred sixty seven thousand three hundred six.

∴ 4,67,306 (Indian numeral form) = 467,306 (International numeral form) = Four hundred sixty seven thousand three hundred six (International numeration).

(ii) Thirteen lakh forty five.

Writing the digits in the place value chart of the Indian system :

So, the number in Indian numeral form = 13,00,045.

Placing the commas according to the International system = 1,300,045.

In International numeration, 1,300,045 = One million three hundred thousand forty five.

∴ 13,00,045 (Indian numeral form) = 1,300,045 (International numeral form) = One million three hundred thousand forty five (International numeration).

Fill in the blanks:

(i) Six hundred four thousand eight hundred forty seven.

= ............ (In International numeral form)

= ............ (In Indian numeral form)

= ............ (In Indian numeration)

(ii) Two million three hundred ten thousand one hundred four.

= ............ (In International numeral form)

= ............ (In Indian numeral form)

= ............ (In Indian numeration)

Answer

(i) Six hundred four thousand eight hundred forty seven.

Writing the digits in the place value chart of the International system :

So, the number in International numeral form = 604,847.

Placing the commas according to the Indian system (after 3 digits and then after every 2 digits from the right) = 6,04,847.

In Indian numeration, 6,04,847 = Six lakh four thousand eight hundred forty seven.

∴ 604,847 (International numeral form) = 6,04,847 (Indian numeral form) = Six lakh four thousand eight hundred forty seven (Indian numeration).

(ii) Two million three hundred ten thousand one hundred four.

Writing the digits in the place value chart of the International system :

So, the number in International numeral form = 2,310,104.

Placing the commas according to the Indian system = 23,10,104.

In Indian numeration, 23,10,104 = Twenty three lakh ten thousand one hundred four.

∴ 2,310,104 (International numeral form) = 23,10,104 (Indian numeral form) = Twenty three lakh ten thousand one hundred four (Indian numeration).

Seventeen lakh ninety five is equal to:

1. 1,795

2. 17,00,095

3. 17,095

4. 170095

Answer

Seventeen lakh = 17,00,000 and ninety five = 95.

So, seventeen lakh ninety five = 17,00,000 + 95 = 17,00,095.

Hence, option 2 is the correct option.

Five million five hundred fifty five thousand five hundred fifty five is equal to:

1. 5,000,555

2. 5,000,55

3. 5,555,555

4. 5,550,055

Answer

Five million = 5,000,000; five hundred fifty five thousand = 555,000; five hundred fifty five = 555.

So, the number = 5,000,000 + 555,000 + 555 = 5,555,555.

Hence, option 3 is the correct option.

In international place value system, we write 10-million for:

1. One crore

2. Ten Lakh

3. Ten crore

4. Hundred thousand.

Answer

From the relationship between the two systems, 1 crore = 10 million.

So, 10 million = 1 crore.

Hence, option 1 is the correct option.

One million is equal to:

1. One crore

2. Ten lakh

3. One lakh

4. Hundred thousand

Answer

From the relationship between the two systems, 10 lakh = 1 million.

So, 1 million = 10 lakh.

Hence, option 2 is the correct option.

Nine crore five lakh forty one is equal to:

1. 945,410

2. 9,05,00,041

3. 9,050,041

4. 9,005,041

Answer

Nine crore = 9,00,00,000; five lakh = 5,00,000; forty one = 41.

So, the number = 9,00,00,000 + 5,00,000 + 41 = 9,05,00,041.

Hence, option 2 is the correct option.

1 million is equal to .............. ten thousand.

1. Ten

2. Hundred

3. One

4. none of these

Answer

1 million = 1,000,000 and ten thousand = 10,000.

Number of ten-thousands in one million = 1,000,000 ÷ 10,000 = $\dfrac{1,000,000}{10,000}$ = 100.

So, 1 million = 100 ten thousand.

Hence, option 2 is the correct option.

Forty five lakh thirteen in Indian numeral form is:

1. 4500013

2. 45,00,013

3. 4,500,013

4. Both 2 and 3

Answer

In the Indian system, starting from the right, the first comma is placed after 3 digits and then after every 2 digits.

Forty five lakh = 45,00,000 and thirteen = 13.

So, the number = 45,00,000 + 13 = 45,00,013.

Writing the digits in the place value chart of the Indian system :

So, in the Indian numeral form, the number is written as 45,00,013.

Hence, option 2 is the correct option.

Four hundred six thousand seven hundred forty eight in International numeral form is:

1. 406,748

2. 406748

3. 4,06,748

4. Both 1 and 3

Answer

Four hundred six thousand = 406,000 and seven hundred forty eight = 748.

So, the number = 406,000 + 748 = 406,748.

Writing the digits in the place value chart of the International system :

So, in the International numeral form, the number is written as 406,748.

Hence, option 1 is the correct option.

Statement 1: As per Hindu Arabic system of numeration 5762983 will be written as: 5,762,983.

Statement 2: As per the International system of numeration 5762983 will be written as: 5,762,983.

Which of the following options is correct?

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Answer

The given number is 5762983.

Statement 1 : In the Hindu-Arabic (Indian) system, the commas are placed after 3 digits and then after every 2 digits from the right, giving 57,62,983 — and not 5,762,983. So, Statement 1 is false.

Statement 2 : In the International system, the commas are placed after every 3 digits from the right, giving 5,762,983. So, Statement 2 is true.

So, Statement 1 is false and Statement 2 is true.

Hence, option 4 is the correct option.

Statement 1: In Hindu Arabic system of numeration 515006200 is read as: Five hundred fifteen million and six thousand two hundred.

Statement 2: In International system of numeration 515006200 is read as: Fifty one crore fifty lakh six thousand two hundred.

Which of the following options is correct?

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Answer

The given number is 515006200.

Statement 1 : In the Hindu-Arabic (Indian) system, 515006200 = 51,50,06,200, which is read as fifty one crore fifty lakh six thousand two hundred — not "five hundred fifteen million and six thousand two hundred". So, Statement 1 is false.

Statement 2 : In the International system, 515006200 = 515,006,200, which is read as five hundred fifteen million six thousand two hundred — not "fifty one crore fifty lakh six thousand two hundred". So, Statement 2 is false.

So, both the statements are false.

Hence, option 2 is the correct option.

Assertion (A): In Hindu Arabic system of numeration 9365217 = Ninety three lakh sixty five thousand two hundred and seventeen.

Reason (R): In Hindu Arabic system counting from right hand side towards left first three digits form one's period, next two digits form thousand's period and next two digits form lakh's period.

∴ 9365217 = 93,65,217

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

Assertion (A) : In the Hindu-Arabic (Indian) system, 9365217 = 93,65,217, which is read as ninety three lakh sixty five thousand two hundred seventeen. This agrees with the assertion, so A is true.

Reason (R) : In the Hindu-Arabic system, counting from the right hand side, the first three digits form the one's period (ones, tens and hundreds), the next two digits form the thousand's period (thousands and ten thousands) and the next two digits form the lakh's period (lakhs and ten lakhs). This is correct, so R is true.

So, both A and R are true.

Hence, option 3 is the correct option.

Assertion (A): In International system of numeration 638452179 = Six hundred thirty eight million four hundred fifty two thousand one hundred seventy nine.

Reason (R): In International system of numeration counting from right hand side towards left first three digits form one's period, next three digits form thousand's period and next three digits form million's period.

∴ 638452179 = 638,452,179

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

Assertion (A) : In the International system, 638452179 = 638,452,179, which is read as six hundred thirty eight million four hundred fifty two thousand one hundred seventy nine. This agrees with the assertion, so A is true.

Reason (R) : In the International system, counting from the right hand side, the first three digits form the one's period (ones, tens and hundreds), the next three digits form the thousand's period (thousands, ten thousands and hundred thousands) and the next three digits form the million's period (millions, ten millions and hundred millions). This is correct, so R is true.

So, both A and R are true.

Hence, option 3 is the correct option.